\newproblem{lay:3_2_37}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 3.2.37}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Ana Peña Gil, Jan. 19th 2014} \\}{}

  % Problem statement
	Let $A=\begin{pmatrix}3 & 1 \\ 4 & 2\end{pmatrix}$. Write $5A$. Is $\det\{5A\}=5\det\{A\}$? \\
}{
   % Solution
	\begin{equation*}
		\begin{array}{c}
			5 A=5\begin{pmatrix}3 & 1 \\ 4 & 2\end{pmatrix}=\begin{pmatrix}15 & 5 \\ 20 & 10\end{pmatrix} \\
			\det\{5A\}=\left|\begin{array}{rr}15 & 5 \\ 20 & 10\end{array}\right|=50  \\
			5 \det\{A\}=5\left|\begin{array}{rr}3 & 1 \\ 4 & 2\end{array}\right|=5\cdot 2=10 \\
		\end{array}
	\end{equation*}
	We see that $\det\{5A\}\neq 5\det\{A\}$
}
\useproblem{lay:3_2_37}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}